Borges, Cervantes & Quine Reconciling Existence Assumptions and Fictional Complexities in Pierre Menard, Author of Don Quixote

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1 William Woof Borges, Cervantes & Quine Reconciling Existence Assumptions and Fictional Complexities in Pierre Menard, Author of Don Quixote By extending quantification definitionally we accomplish the introduction of fictions; but we may still add further definitions in order to make our fictions behave more like real entities i.e., in order to make our fake names amenable to various contexts in which genuine names occur We cannot, even in our transcendent universe, allow a new entity to be determined by every formulable condition on entities; this is known to lead to contradiction in the case of the condition (xòx) and certain others. A transcendent universe transcends the controls of common sense. W. V. O. Quine, A Logistical Approach to the Ontological Problem. T he converse philosophical problems of ontological commitments ( what is? ) and negative existential propositions ( what isn t? ) originate in Plato s Parmenides and centre on the question as to how we can, in any sense, understand the non being or non existence of an entity without contextualizing it according to the properties and characteristics of existence. W. V. O. Quine has been particularly concerned to frame the issue in terms of quantificational logic, arguing that ontological commitment must be recognized not through proper names but through the quantification of variables. This allows us to range over a large domain of real entities (to whose existence we commit) which may be instantiated as needed in particular cases. In Quine s view, we may understand the non existence of an entity without incurring any subsequent confusions between naming and meaning whereby we must in some sense acknowledge some element of being in a non existent entity in order to arrive at its meaning. By Variaciones Borges 7 (1999)

2 192 William Woof granting that the mental idea of a fictitious entity must be conceded some form of ontological status, we open the door to scenarios of possible worlds, or what Quine refers to as a slum of possibles, which in turn is a breeding ground for disorderly elements ( On What 4). 1 Meaning does not presuppose existence and in conjunction with this assertion, we must be wary of granting ontological status to universals, properties or attributes. In short, Quine s project entails the rejection of both second order logic (which allows us to quantify over properties) and quantified modal logic (which may distort reference to actual entities through the introduction of modal or essentialist considerations). As Pascal Engel states: According to Quine s thesis, the notions of nominal reference, of existence, of predication, of truth and of identity are so closely tied to one another and to the notion of objectual quantification, that it is impossible to analyze any one of them without using the others. (77) However, Quine s theory, (or, more specifically, Bertrand Russell s Theory of Descriptions, which has come to be known as the no name theory of singular terms and which Quine stipulates as the only source of such terms) does not facilitate any meaningful analysis of empty sets that may be relevant to works of fiction. Hamlet killed his uncle is a false assertion (since there was no such historical personage as Hamlet) and yet it is true in the context of Shakespeare s play. We can address this problem through free logic, or logic that facilitates reference for non denoting expressions, but Quine is reluctant to venture into deviant logics because of the fact that we lose the rewards of staying within the bounds of standard grammar (Philosophy 79), those rewards being extensionality, efficiency, completeness. But we are still left with a problem with respect to fictional works that now seem to be bereft of the stricter modes of logic for the purposes of literary analysis. What we need is a procedure for assigning truth values within fictional contexts. This problem may be less of an issue for logic per se (whether logical form follows grammatical form) than for theories of meaning themselves. Robert Scholes notes that Plato s denunciation of poetry as beautiful lies would not rule out a level of meaning at which fic- 1 It can be contested whether or not Quine objects to the mental idea of a fictitious entity as such. His claim is likely restricted to a more modest assertion as to whether meaningful expressions can designate nonexistent entities. (I am grateful to Dr. W. Abbott for pointing this out.) This thesis will proceed on the conclusion that his essay On Mental Entities lumps together all mental entities as a hindrance to science (226).

3 Borges, Cervantes and Quine 193 tion could be deemed to be true in terms of its depicted situations and the moral truths it conveys and yet be false in the literal sense (119). Scholes then goes on to note that on the basis of such a possible level of meaning, Aristotle detected an advantage in verisimilitude and mimesis, that reconstruction of reality which posits universal forms of action applicable in all possible depictions of reality. As Scholes notes, Aristotle was interested in distinguishing poetry from history for the purposes of demonstrating the applicability of the laws of probability across all possible worlds: The superiority of poetry over history was its ability to represent not actuality itself but the typical. Whereas history was limited to describing events as they actually happened, poetry could present hypothetical events as they might well happen. The agents in poetic action were universal in that they said and did things one would expect from men of certain types. Their actions were consistent in that they followed laws of probability and necessity. Its consistency, its universality, and its representation not of actuality directly but of the laws governing actuality constituted the superiority of poetry over reporting. ( ) 2 However, the domination of postmodernism in literature over the past sixty years has resulted in the introduction of literary works that lack (or deliberately confuse) clear delineations between actual and possible worlds. Among these works is Jorge Luis Borges s short story, Pierre Menard, Author of Don Quixote. Borges s story depicts the fictitious character of Pierre Menard, a philosophical dabbler and literary dilettante who, according to the story s narrator, believes that without recourse to copying or transcription of any sort he can produce a word for word duplication of Don Quixote, the seventeenth century masterpiece of Spanish literature. Menard imagines that he can accomplish this reconstruction entirely through 2 Scholes notes that poetry, history and philosophy were fused in the epics of Ancient Greece, with the result that philosophers such as Metrodorus of Lampsacus, a disciple of Anaxagoras, searched great works of poetry for allegorical meanings by which physical meanings were assigned to the characterizations of both humans and gods (Achilles represented the sun, Helen the earth, etc.) in a massive system of symbolic representation. As Scholes notes: This tradition of Homeric allegoresis was well established at the time of Plato s birth, and it constituted, by the time he came to write the Republic, an important element in Greek philosophical speculation. (118) Aristotle s attempt to separate poetry and history will be examineded later in this paper in the attempts of Cervantes to fuse them together. (Novalis attempted a similar enterprise.) The creation of vast systems of symbolic representation will be reflected in the philosophical enterprises of Raymond Lull.

4 194 William Woof his own experiences and without necessarily assuming the identity of the text s author, Miguel de Cervantes. The story is narrated by a pompous, naive admirer who lauds Menard s preposterous enterprise as praiseworthy, certainly praiseworthy to no lesser degree than other intellectual exercises, all of which are deemed useless. At the end of story, he foolishly indulges the fantasy of imagining literary works being produced by other authors in anachronistic sequence and concludes with the Platonic notion that every man should be capable of all ideas. 3 Into this superficially simple story, Borges has built numerous difficulties and complexities, much of which bear on our logical comprehension of fictional undertakings and most especially that text which serves as the story s source. Don Quixote, considered to be one of the most important precursors of the modern novel, is fraught with paradoxical constructions and violations of the principles of verisimilitude. The character, Don Quixote, transforms the stories of chivalry and knighthood he reads into absurdly caricatured and literal recreations: wind mills become the frozen form of giants, inns become castles to be seized. At one point in the second book, Quixote even attacks the puppets in a puppet show under the delusion that the historical personages from legend represented by the puppets had come to life (Book II, 171). The character is thus deemed mad because of his inability to distinguish life from literature or, more exactly, because he assumes the ironic ability to conflate wisdom with knowledge, sanity with insanity. (It is the wise man who appears insane because the ideals he sees as essential for civilised progress seem ludicrous to his fellows.) In modern critical evaluations, Quixote s imitations of chivalric bravery are compared to the process of verisimilitude itself: the hero, a born imitator, defines himself by a function clearly analogous to literature, which (...) pretends only to reproduce, represent, and imitate some real aspect of life (Robert 113). In Don Quixote, Cervantes attempts to blur the distinctions between the form of the fiction and its content. Cervantes serves himself up as a character in his own work, as we discover one of his books (Galatea) in Quixote s library during an inspection by the local curate and the barber, the former claiming a direct acquaintance with the author within the context of his own book (I, vi, 86). The text of Don Quixote is found to exist within the book itself in the form of a manuscript written by a 3. Todo hombre debe ser capaz de todas las ideas (OC 1:450).

5 Borges, Cervantes and Quine 195 Moor, Cid Hamete. Cervantes thus denies the authorship of his own text within the very text he has written, thereby imbedding within the book a paradox of self referentiality (and thus incurring an incidence of Russell s paradox, which, as noted by Quine, exposes us to the danger of a transcendent universe transcending the controls of common sense ). At one point in the text, we find Don Quixote and Sancho Panza reading Cid Hamete s historical text, quizzically disputing as to how the author could have known about their actions when they were alone. If we imagine this text as projected into the infinite regress entailed by logical consequence, we would presumably discover them reading about themselves reading the text, a circumstance of self referentiality certain to leave them even more puzzled. Borges s story of Pierre Menard extends the modal context of Cervantes s fictional world by creating in the title character a replication of Quixote himself. Like Quixote, Menard is an imitator, one who acts out fiction in real life, but it is an acting out which pertains to form, to the acts of creation of the books he reads rather than to their contents. Like Quixote, he too possesses his own library, but the fantasies he acts out are authorial rather than chivalric. The explicit connections between Menard s study of metrical laws, paradoxes, symbolist logic and symbolist literature will be analyzed at greater length in the course of this paper, but for now it is important to note that Borges has taken the complexities of Cervantes s work its blurring of modal distinctions between actual and possible worlds, its manipulations of self referential paradoxes and placed them in a twentieth century context that both enhances and transforms these elements. What may become apparent from a comparative study of Cervantes and Borges are the differences and even the incommensurabilities between historical periods which affect the way fictional works can be interpreted, logically analyzed or subjected to literary criticism. The satirical thrust of Don Quixote was directed at the plethora of false historical writings which abounded in Cervantes s day. The book repeatedly asserts itself as a true history, in spite of the fact that it acts out a drama already written as an historical record by a Moorish author who by virtue of his race would have been regarded in Cervantes s day as a liar (Wardhopper 80 94). Borges, aware of this satirical intent, selects the following passage from Don Quixote, a description of truth as assiduously copied by Menard, as indicative of the irony latent in two different interpretive ascriptions:

6 196 William Woof truth, whose mother is history, who is the rival of time, depository of deeds, witness of the past, example and lesson to the present, and warning to the future. (Ficciones 36) 4 The pompous narrator of Borges s story, oblivious to the satirical intent of Don Quixote and the consequent irony contained in the passage, dismisses Cervantes for his mere rhetorical eulogy of history. 5 Menard, on the other hand, is praised for invoking William James s famous and controversial assertion: Truth happens to be an idea. It becomes true, is made true by events. (James 201) For James, the truth of a proposition was determined from the process of its verification, the same point made by Cervantes in his attack against bogus historical accounts and thus applicable by extension to Menard s bogus re enactment of Don Quixote. But Borges is also making a more important point. Identical passages in literature can be subject to significantly different interpretations over time and this has been particularly true of Don Quixote. According to eighteenth century standards of verisimilitude, the central character was originally interpreted as an absurd, pathetic buffoon incapable of making distinctions between fantasy and reality, a view conducive to the increasingly scientific worldview of the seventeenth and eighteenth century. In the twentieth century, when deconstruction, fallibilism, existentialist concepts of the absurd, and Feyerabend s denial of scientific method have become the norm, Quixote is seen as a tragic rather than a comic figure, a representative of modern man. This modern view is captured by Charles Aubrun: He [Quixote] knows that it is necessary to practice excess in order to find his limits and know himself. By turning reason upside down, by exposing its other side, madness, Don Quixote bears witness, in his way, to the philosophic trend which would break down the extremes of logic, the sophistries... of Aristotle s epigones, the abstract mechanical rationalism of human reality. (60) Borges understood the sorties of madness against the extremes of logic. His essay on paradoxes concludes with this exhortation: Let us admit what all idealists admit: that the nature of the world is hallucinatory. Let us do that which no idealist has done: let us look 4 la verdad, cuya madre es la historia, émula del tiempo, depósito de las acciones, testigo de lo pasado, ejemplo y aviso de la presente, advertencia de lo por venir (OC 1: 449). 5 un mero elogio retórico de la historia. (OC 1: 449)

7 Borges, Cervantes and Quine 197 for the unrealities that confirm that nature. We shall find them, I believe, in the antimonies of Kant s and in Zeno s dialectic. (Other 114) 6 It must be noted that Borges is here granting these concessions in order to refute idealism, but he is also fascinated by the possibility of discovering an ancillary value in practicing excess, in setting up within his fictional domains the opportunity to search for unrealities. If the scientific method of the modern age is to be dominated by loss of method and uncertainty principles, then Borges finds no difficulty in developing fictional characters who pursue unprovable conjectures, especially those that relate to unreal or quixotic ventures. Readers and critics who accept the scientific worldview of the twentieth century are far more likely than their seventeenth and eighteenth century counterparts to take such ventures seriously and less likely to dismiss them out of hand as comic buffoonery. In extending the boundaries of Don Quixote into a modern context through enhancements of traditional narrative devices which become used for blurring distinctions between fact and fiction, Borges very likely considered the possibility that his story would not only mirror the process and the content of Cervantes s masterpiece, but the history of its critical evaluation as well. His achievement in creating in Menard a character who mimics Quixote s absurd habits of imitation might be matched by a transformation in the critical evaluation of Menard from a comic to a tragic figure (a change which has not yet taken place). If such a change occurs, if we come to see Menard as a tragic figure, then we must consider the possibility of taking him seriously in the same way that literary critics now take Don Quixote seriously. We must thus come to appreciate the assault of madness on the extremes of logic ; we must try to accept a tentative postulation of the hallucinatory nature of the world. Thus, the objective of this paper will be the provision of a philosophical basis for altering the current literary evaluation of Borges s story. Pierre Menard, Author of Don Quixote, is not, as is usually depicted in the critical literature, the portrayal of a literary plagiarist whose visible writings constitute a pretentious dabbling or some kind of displacement of other writings (Borinsky 154). Rather, the story can be seen to constitute a philosophical thought experiment of considerable com- 6 Admitamos lo que todos los idealistas admiten: el carácter alucinatorio del mundo. Hagamos lo que ningún idealista ha hecho: busquemos irrealidades que confirmen ese carácter. Las hallaremos, creo, en las antinomias de Kant y en la dialéctica de Zenón (OC 1:258).

8 198 William Woof plexity, one that establishes Menard in Borges s pantheon of intellectually sophisticated impostors. The standard evaluation has been long established because Menard s claims to have written Don Quixote are prima facie absurd and Borges enhances this view by using the traditional narrative device of a pompous and foolish narrator who lavishes extravagant praise on his subject and appears to ignore the more comic implications of Menard s activities (e.g., his burning of his preliminary manuscripts). Once Borges has established this mindset in the reader, a tendency is created to bypass or gloss over the visible works in Menard s oeuvre in a similar manner and thus the possibility that Menard is using these works to establish a philosophical justification for his claim to authorship of Don Quixote can be missed. This paper will attempt a detailed examination of these visible works not only to show the nature of the justification sought by Menard but also demonstrate (in conjunction with other works by Borges) how this justification sets up a philosophical thought experiment which is valuable in itself. The visible works are largely focused on three areas. The first covers the history of symbolic logic: from its origins in Raymond Lull s primitive attempts to build systems of symbolic representation, through to the enhancements of this enterprise in the works of Wilkins, Leibniz and Boole, and finally to the difficulties faced by logicians in the paradoxes identified by Bertrand Russell and others. The second area covers the history of the literary movement known as Symbolism while the third presents an analysis of the classics of chess and poetry from Spanish literature. Menard s narrator does not give us sufficiently detailed abstracts for any of these visible works, so much of the work of this paper will be given over to elucidating their subject matter and the derivations from their philosophical sources. When this is done, it should be apparent that the complex of ideas that can be generated from the visible works are sufficient to give legitimate philosophical justification to Menard s enterprise, a justification constructed in terms of a thought experiment. By exploiting the historical philosophical debates between realism and idealism (debates traceable from the visible works), one can build a case for justifying Menard s absurd claims to authorship of Don Quixote, a case founded on establishing the novel as a set of independent concepts subject to independent discovery by different men and thus not constituting the unique invention of a particular individual. The singular weaknesses of realism and idealism to be exploited are the issues of how ideas themselves can have independent existence (the weakness of idealism) and the failure to move from certainties of common sense to certainties of epistemology (the weakness

9 Borges, Cervantes and Quine 199 of realism). Menard s project falls through the cracks between realism and idealism by exploiting differences in worldview and in standards of literary evaluation between different historical periods and by demonstrating that all symbolic ascriptions, whether pertaining to logic, literary movements or methods of classification, are necessarily arbitrary. Thus, the value that Aristotle detected in the verisimilitude of fiction (i.e., its facility for representing the typical rather than just the actual) created a corresponding problem: how to establish true statements within fictional contexts, especially fictional contexts as used both by Symbolists and by Cervantes in Don Quixote that blur the distinctions between actual worlds and real ones and that give support to Menard s enterprise through the recognition of one s own work in the work of one s literary predecessors. This problem has a very serious historical dimension, since the standards of literary criticism that govern the understanding and application of verisimilitude have undergone transformations analogous to those in scientific worldview. As previously noted, this concept of verisimilitude has functioned as a correlative to concepts of universality and probability. In modern theory, it links together rationality and belief with assessments of states of affairs relating to the frequency of occurrence of events. In Aristotle s judgement, the quality of fiction was based on the degree of its correspondence to real life in terms of its probability or necessity (Ramsey ). In Cervantes s period, the term was used to praise highly standardized characters and situations. (Shakespeare was criticized on these grounds.) In Borges s era, the term had been taken over by the New Critics to praise the use of paradox and irony in poetry and fiction (Ramsey ). The transition to postmodernism is marked by the change from singular to multiple versions of literal truth which can co exist simultaneously. Here, then, we are brought back to Quine s approach to quantificational logic. In many respects, he advances the approach taken by Bertrand Russell in withholding logical consideration from fictional worlds (all propositions related to which were deemed to be false de facto), and it is noted that both Russell and Quine take a dismissive approach to the notion of permitting quantification to modal logic. Yet the development of semantics for modal logic and the possibilities it has opened for the application of truth conditions to intensional contexts has led to serious consideration of the reality of possible worlds and increased questioning of Quine s standards of ontological com-

10 200 William Woof mitment. Modern logicians such as Stephen Read and Pascal Engel have taken note of the increasing interest in applying logic to what Engel describes as alternative histories of the real world (151), which would include those falling within a fictional domain. This would suggest that we need a method of dealing with the as if or the virtual ontologies of fictional worlds in a manner similar to that of real world ontology. All that is required are logical enhancements which allow us to distinguish true statements within fictional contexts. As Stephen Read points out, we (or at least literary critics) need to be able to talk about the activities of fictional characters in a meaningful way. We need to be able to assert that King Lear was the father of Regan and Goneril is a true statement within the context of Shakespeare s play. Read suggests the use of a fictional operator to clearly contextualize the fictive world as distinct from the real one, such that we could make meaningful statements about such domains. But, as Read goes on to note, such an operator presents enormous difficulties, since we would require a manifold of such operators to cover the various permutations of fictitious worlds: e.g., parodies of Hamlet, in which it might be true that Hamlet and Laertes do not kill each other (127). Problems of this sort had been seriously considered by Quine, who harboured deep suspicions of propositions (covering all expressions of belief and desire) as bearers of meanings. But, as Pascal Engel points out, Quine s radical rejection of propositional meaning will cost us our ability to conduct common sense discussions in the absence of finer differentiation of what was believed, understood or said. 7 On this basis, Engel claims that he should be able to assert the truth of Einstein s energy equation without needing to understand either its proof or its propositional construction. This is a claim of moderate realism, and one that echoes that of Menard, who also wishes to assert the truth of his absurd claim without provability; and what is fascinating about this claim is its obvious failure to pass the test of common sense while avoiding dismissal on any epistemological grounds. The nature of Borges s thought experiment in Pierre Menard should now be examined in more detail, as the story provides evidence that Menard sought out (and was correct in accepting) philosophical justifi when two people say something, must we refuse to talk about the contents of what they are saying or to admit that they could be saying or believing the same thing? If propositions are only terms that are convenient to designate what is true or false, what is believed, understood or said, the notion has a theoretical interest which is not negligible (Engel 34).

11 Borges, Cervantes and Quine 201 cation for his enterprise. The first indication of this attempted justification is found in the distinction made by the narrator between Menard s visible and subterranean works. While the latter consists solely of the infamous Don Quixote project, the former is taken up with studies of literature and philosophy that are (apparently) seriously motivated although often pedantic and imbued with unintentionally comic undertones. The alert reader will note the direct references to the writings of Leibniz and Russell and remember that it was Russell himself who was responsible for detecting that Leibniz had both an invisible philosophy (one he kept hidden from the public) as well as the visible one which was believed, before Russell, to have encompassed the full scope of his philosophy. 8 According to Russell (History 591), it was Leibniz who discovered mathematical logic a century and a half before George Boole first brought algebraic notation to logic and successfully devised an algebra of propositions in (Leibniz had kept this secret because he didn t think his contemporaries would believe findings that contradicted Aristotelian logic, and he feared the censure that would follow if he published them). Leibniz had devised this logic to support his Characteristica Universalis, 9 a scheme by which metaphysical problems could be calculated and solved in a manner similar to that of mathematics. The logic was based on a scheme of conceptual enumeration organized according to a set of rules paralleling those of language or grammar and this system bore a marked resemblance to schemes already put forward by Descartes (in 1629) and John Wilkins (in 1688). Again, the alert reader will note that Menard s visible works include essays on Boole s symbolic logic, on Leibniz s Characteristica Universalis and on certain affinities between the works of Descartes, Leibniz and Wilkins. It must be concluded that in seeking to advance his project, Menard is hoping for an historical payoff in the almost certain transformation of the contemporary worldview, the hope that what would today be regarded as a patent absurdity will come to acquire a future 8 Russell published his results in A Critical Exposition of the Philosophy of Leibniz (1900). Russell notes that Leibniz had communicated his esoteric philosophy to Antoine Arnauld in a series of letters, but that its significance was overlooked. This esoteric work was published by Louis Couturat in two volumes (1901, 1903). 9 For purposes of convenience (if not for strict accuracy), this essay will use Leibniz s neologism characteristica universalis to refer both to the system of universal notation (which, strictly speaking, is what the characteristica covers) and the consequent system for formal analysis and calculation, the calculus ratiocinator. I am presuming that Menard s monograph would cover both of these aspects.

12 202 William Woof legitimacy. It can be argued that Menard seeks a personal identification with Leibniz as much as he does with Cervantes. The notion of affinities brings out the second justification for Menard s enterprise, that of simultaneous and/or independent discovery. Leibniz s discovery of infinitesimal calculus coincided with that of Newton s. Russell and Peano had independently founded logicism. Frege and Peirce had separately developed theories about quantificational logic. Such notions of affinity are important to Menard s thesis that he and Cervantes could independently discover Don Quixote, although the difference between the discovery of a set of theorems and the entire set of concepts that comprise a work of fiction of the length of Quixote is obviously not easy to bridge. This introduces the problem of vagueness, or that of the sorites paradox: the difficulty, that is, of drawing the line with respect to the complexity of concepts such that we could accept that one set but not another was subject to independent discovery. Both Russell and Frege believed that vagueness points out a weakness in ordinary language, a weakness that suggests the need for an ideal language of concepts (a parallel to Menard s aspiration for an ideal vocabulary of poetic concepts). It is also interesting that Russell believed that human mortality exerts only an artificial limitation on our ability to discover and verify knowledge a mere medical impossibility (Problems 23), thus suggesting that Menard could duplicate Cervantes s achievement if granted a lifetime long enough to accumulate the necessary experiences. Or, as Menard puts it, My undertaking is not essentially difficult, I would only have to be immortal in order to carry it out (Ficciones 33). 10 Thus, the philosophical justification that Menard undertakes in support of his enterprise consists of a reconstruction of the history of symbolic logic which came to fruition in the nineteenth and early twentieth century, a history whose roots can be traced back to the thirteenth century attempts of Raymond Lull to develop a symbolic vocabulary. His Ars Generalis Magnus was the precursor to the subsequent efforts of Wilkins and Leibniz, and elaborated a form of algebraic notation designed to create a universal language for expressing metaphysical principles. Menard then follows this theory into the later work of work of John Wilkins, who devised a methodology for developing a vocabulary such that each word would define itself through the symbolic representa- 10 Mi empresa no es difícil, esencialmente ( ) Me bastaría ser inmortal para llevarla a cabo (OC 1:447).

13 Borges, Cervantes and Quine 203 tions of concepts. By constricting meaning in this way, Wilkins seems to anticipate the Grelling and other semantic paradoxes that require the stipulation of a metalanguage in which the existence of paradox is rendered impossible. 11 Menard is also led into a lengthy consideration of the problem of paradoxes, as his one full length book, Les problèmes d un problème (a takeoff on works by both Russell and James, both of which are entitled The Problems of Philosophy and address the problems of paradox), deals at length with Zeno s paradox of Achilles and the tortoise and the various solutions that have been developed over the centuries. Borges himself was fascinated by this paradox and had provided a brief history of the purported solutions in his essay, Avatars of the Tortoise (Other). Aristotle s solution would have proved highly instructive from Menard s point of view, since the Aristotelian refutation entails collapsing distinctions between forms and the objects represented. Aristotle postulates that if two or more men share properties that originate in a form, then such an archetype must be a third man, who along with all the other men represented by the archetype must be represented by a new form, and so on. As Borges notes: Two individuals are not actually needed: the individual and the class are enough to determine the third man postulated by Aristotle. Zeno of Elea uses infinite regression to deny movement and number; his refuter uses infinite regression to deny universal forms. (Other 111) 12 The content of the chapter of his book that Menard dedicates to Russell provides an interesting topic of speculation, since Russell (at an early point in his career) used universal forms to support his own arguments in favour of realism. He had devised a response to Plato s criticism in the Parmenides that the one cannot be unified since it partakes of being and must therefore be plurality. Russell had argued that the concept of being as applied to numbers is vague, since numbers don t have real existence (OC 1: 255n). Of greater interest is the dispute over realism that centres on the version of the Achilles/tortoise paradox put forward by Lewis Carroll in his fable, What The Tortoise Said to Achilles ( ). Carroll de- 11 Grelling s paradox is constructed around the sort of built in structure of meaning used for autological words (i.e., short is a short word). 12 En rigor no se requieren dos individuos: bastan el individuo y el género para determinar el tercer hombre que denuncia Aristóteles. Zenón de Elea recurre a la infinita regresión contra el movimiento y el número; su refutador, contra las formas universales (OC 1: 255).

14 204 William Woof picts a conversation between the Tortoise and Achilles after their famous race in which the tortoise reconstructs one of Euclid s syllogisms, i.e., the demonstration that two sides of an equilateral triangle must equal the third. The tortoise refuses to accept the syllogism unless the logical law of validity (truth of premises guarantees truth of conclusion) is inserted as an additional premise. But the tortoise will then not accept the new syllogism unless an additional premise is inserted: i.e., the same law of validity only expanded to include three premises instead of the two previously used. The tortoise thus creates an infinitely expanding argument whose conclusion can never be accepted by inference. This new version of the paradox turns on the same category/membership distinction as the previous rendition ( the third man ), but this time with a new twist. In Carroll s story, the distinction being collapsed is that between laws (in this case the laws of logic) and the states of affairs they govern. As Pascal Engel points out, what is at stake here is the acceptance of logical necessity, of an understanding of logical truths as a special category of non empirical, non natural facts bearing on an independent reality. 13 The tortoise takes the anti realist position of refusing to accept such logical laws as self evident and insisting that they be included as part of the proof of the very states of affairs to which they are to be applied. This point is brought out by Jerry Fodor, who makes his case for realism with respect to machine intelligence by citing Carroll s example: There is a point of principle here one that is sometimes read in (or into) Lewis Carroll s dialogue between Achilles and the Tortoise: not all the rules of inference that a computational system runs can be represented just explicitly in the system; some of them have to be, as one says, realized in the hardware. Otherwise the machine won t run at all. (23) Thus, Menard, who makes his treatise on Carroll s paradox the one book length item in his visible works, is right to quote Leibniz s warning against believing the tortoise. Menard s enterprise in one respect depends on a realist conception of Don Quixote as an abstract entity, as an independent set of integrated concepts that one discovers rather than invents and as a discoverer, Menard can make an equal claim to authorship with Cervantes. But the realist conception will not work without clear distinctions between types of attributes, between univer- 13 The propositions of logic are necessary because they are objective in the sense that they describe a universe of facts or of situations that could not fail to exist. (Engel 257)

15 Borges, Cervantes and Quine 205 sals and particulars, between forms and appearances, between the analytic and synthetic, between laws and the states of affairs that they govern. Menard s fascination with universal languages and the laws governing the use of such languages reflects a similar ambition on the part of Russell and Frege. The difference between Russell and Menard is the fact that the former sought out a universal language for the purposes of clarity and for avoiding the vagueness that Menard needs to justify his claims by way of the sorites paradox. Menard, on the other hand, needs both the realism and the paradoxes that go with them, and so his ideal vocabulary of concepts is a poetic and not scientific one. This is the heart of the thought experiment that Borges creates: if realism postulates a universe of logical truths which are applicable (in Leibniz s view) to all possible worlds, then how do the same principles of realism also justify Menard s absurd and solipsistic enterprise? Borges is interested in determining whether or not the answer to this question lies in the ideal world itself and thereby involves Menard in the same deception used by the tortoise: the failure to separate logical laws from the propositional constructs to which they apply. (Thus Menard s warning against the tortoise is ironic: the tortoise is giving away Menard s game by calling into question the same assumptions of the a priori, given nature of logical truths that underwrite all versions of realism, including Menard s.) As a result, Menard is fascinated by the history of symbolic logic and seems to follow it from its alchemic, scholastic origins in Lull through nineteenth century attempts to establish logicism as an absolute science and finally to its ultimate failure in paradox. The period of Menard s writings as recorded in the visible works are coincidental with the period of Russell s major writings and seem to follow the philosopher s gradual turn away from realism. (By the 1930 s, Russell had adopted the belief that objective knowledge is largely based on interpretation and a holistic consistency of one s belief system. Thus, Menard s narrator is justified in his assertion that a philosophical doctrine is in the beginning a seemingly true description of the universe (37) 14 which decays and degenerates over time.) Yet Menard s visible works not only demonstrate his fascination with symbolist logic but an equal and contemporaneous fascination with the symbolist movement in literature. Menard himself is described by his pompous narrator as a Symbolist, 14 Una doctrina filosófica es al principio una descripción verosímil del universo (OC 1: )

16 206 William Woof and the visible works evidence this through his writings in Symbolist journals and his friendship with the Symbolist poet, Paul Valéry. Symbolism, as a literary movement, advocated not the rigid designation of fixed meanings, the primary tenet of symbolic logic, but the advancement of multiple, metaphoric meanings, often with mythical or iconographic overtones. 15 The movement gives strong impetus to Menard s project since it advocates a sort of déjà vu in reading or interpreting literary works. Baudelaire, one of the founders of Symbolism, noted that reading the works of Edgar Allan Poe (one of the authors cited by Menard s narrator) for the first time triggered a recognition of literary works he had already imagined writing. The movement was also characterized by its confusion of the imaginary world with the real and this conflation was at least partly due to the change in the literary assessment of Don Quixote that originated in Symbolism s precursor movement: German Romanticism. 16 Finally, Symbolism shared with symbolic logic the obsession for developing a universal language based on altering basic grammatical rules. 17 No such language is, of course, possible since, as is made clear in the story of Achilles and the Tortoise, there is no way to separate the rules of a language from its meaningful content without invoking a metalanguage or type theory. Quine himself accepts that there is no ultimate grounding for the rules of logic and that even the basic rules of bivalence cannot determinably eliminate such nuisances as the sorites paradox. He supports bivalence on the grounds that it is right for us to reason as if our terms were precise, ( Bivalence 92) and it is thus incumbent for scientists to try, as far as possible to achieve the type of precision in measurement that is normally conducive to classical logic. 15 Hans Georg Gadamer was responsible for bringing this movement back into the realm of philosophy through his advocacy of multiple meanings and his perspectival, non objective focus on interpretation. 16 Luis Murillo notes the changes in the literary assessment of Don Quixote that had occurred prior to the end of the nineteenth century, addressing the multiple antithesis discovered in the book, illusion and reality, idealism and common sense... that ultimately centred on the complex irony latent in the text (48 49). 17 At least one Symbolist, Francis Vielé Griffin, shared with Menard the desire to abolish the Alexandrine, the classical verse metre of French literature. The Alexandrine was the classical form of French verse (twelve syllable line) and its use was subject to strict rules, adapted by each literary movement in French histroy. The Valery poem mentioned by Menard, Le Cimetiere Marin, was deliberately written in decasyllables to achieve the same effect as the Alexandrine, so Menard s attempt to rewrite it in Alexandrines would have effectively ruined it.

17 Borges, Cervantes and Quine 207 But this as if leads to a problem pointed out by Jacques Derrida in his analysis of Kant s categorical imperative (190): i.e., the need to postulate the as if entails the postulation of a fictitious realm without any standard logical rules to govern such a realm. So although Quine would argue that we should be able to indicate or at least estimate an exact point along the spectrum of human concepts, a determinate threshold beyond which the complexity of idea clusters would constitute a unique and inimitable achievement of a single individual, the fact remains that we can only assert such a truth without any claim to its provability. We intuitively understand our ability to deal logically with both actual and fictitious entities while having no explanation for the paradoxes that such activities engender. We have no airtight refutation of Menard s project. This project builds on the difficulties of understanding and analyzing fiction in a logical manner. Even classical, realistic fiction that functions in a straightforward, veridical manner requires a considerable intuitive grasp of the principles of free logic, quantification and probability theory in order to gain a Quinean precision applicable to any knowledge claims that could be made on behalf of fiction, specifically the differences between actual and fictitious entities. But as we have already noted, the Menard story exceeds the verisimilitude of classical fiction and complicates the paradoxes of the Don Quixote story it subsumes. As previously discussed, the fundamental paradox centres on the paralleling (through the sorites paradox) of Menard s claim to independent discovery of the novel with the independent discovery of scientific concepts. But Menard s separate claim to personal identification with both Cervantes (explicitly) and Don Quixote himself (implicitly, through his quixotic behaviour) also extends the fictional world of Don Quixote into a secondary fictional realm which is continuous with the original. Don Quixote itself is based on a set of paradoxical structures: the first part of the novel is a written document for characters in the second part to read (although Part I was allegedly written after the events of Part II) and we find Don Quixote and Sancho Panza reading about actions that they committed while alone. (So we thus have the possibility of infinite regress through Quixote as a character in the novel he is reading coming across a passage where he would depicted as reading the novel he is reading). The fact that Menard is extending this fictional world outward into his own world (which is exactly what the Don Quixote character does with his own library and its tales of chivalry) is captured when Borges takes

18 208 William Woof note of Menard s conviction that he can arrive at Don Quixote through his own experiences: This conviction, let it be said in passing, forced him to exclude the autobiographical prologue of the second part of Don Quixote. To include this prologue would have meant creating another personage Cervantes but it would also have meant presenting Don Quixote as the work of this personage and not of Menard. He naturally denied himself such an easy solution. (33) 18 Apart from the obvious humour (Menard s denial of personal identity with Cervantes and his claim to arrive at Don Quixote through his own experiences means he can no longer share authorship with Cervantes but must deny Cervantes the authorship of his own work), Menard claims that he must avoid Cervantes s passages of direct self reference (the autobiographical section in question refers to Cervantes s denunciation of a writer who wrote a fabricated version of his story under the name of Don Quixote), although it is clear that such an avoidance means that he will have to give up arriving at Don Quixote through his own experiences (on pain of excluding the passage in question and thus writing a different novel). Menard must revert to his first idea of sharing personal identity with Cervantes in order to participate in such passages of self referentiality and thus extend them outwards into his own world. (Such passages are humorous in their own right solely within the context of Don Quixote since Cervantes had set up Cid Hamete as the author of the work. He then steps out of the fictional context to create an authorial intrusion into the text through which he claims back ownership of a text whose authorship he had already denied.) We thus have Menard extending a fictional context through an absurd authorial intrusion of his own that mimics the genuine authorial intrusion (thereby extending his own fictional context) inserted in Don Quixote by Cervantes himself. The confusions created by these shifts of context within fictional domains are the subject of the various semantic paradoxes, which function by means of self reference and must be eliminated in formal logic through the imposition of type restrictions, such as those introduced by Russell. This type theory entails the establishment of hierarchies of properties such that first order properties are separated (for purposes 18 Esa convicción, dicho sea de paso, le hizo excluir el prólogo autobiográfico de la segunda parte del don Quijote. Incluir ese prólogo hubiera sido crear otro personaje Cervantes pero también hubiera significado presentar el Quijote en función de ese personaje y no de Menard. Este, naturalmente, se negó a esa facilidad. (OC 1:447)

19 Borges, Cervantes and Quine 209 of logical analysis) from second order properties, second order properties from third order, and so on. Type theory found its counterpart in Tarski s material adequacy condition, which had the same effect of banishing paradoxes of self referentiality through the creation of a metalanguage which, in turn, succeeds by making the paradox inexpressible in the metalanguage. The point driven home by Borges in Pierre Menard is the fact that fictional worlds, which are difficult enough to subject to logical analysis in their classical forms, require a similar hierarchy of domains to protect against these same forms of self referential paradoxes. Frederick Copleston notes (431) that one consequence of this structure of hierarchies is the fact that we can no longer speak in terms of the world or the totality of languages, since by definition we can no longer have a complete world or a language which subsumes all the rest, for such a class of all classes cannot (without paradox) be an entity in itself. Such hierarchies would have to be infinite in number. 19 This notion fascinated Borges, who in his essay, The Total Library (Reader 94 96), imagined a library of infinite concepts which would include an accurate catalog of the library and since such an infinite catalog would be an impossible construct, a Cantorian power set larger than the infinite library itself the proof that the catalog is fallacious (96) the library itself becomes a paradox: a self contradictory entity whose existence is impossible and unprovably so, since it is still a conceptually possible entity (i.e., it is possible to imagine an infinite sequence of concepts in which each individual concept can be linked isomorphically to a catalogue entry in a library). It has been previously noted that one of the main themes of Don Quixote centres on the nature of the conflicts between historical reality and the idealism of fiction, and this theme is worked out structurally in the novel through the use of paradoxical constructions that conflate real and imagined worlds within the context of the novel itself. Don Quixote extracts from his books of legends and romances a set of idealized, chivalrous goals that are absurdly acted out in real life. It was Borges s achievement to realize, in the construction of Pierre Menard, that this conflict between realism and idealism could apply not only to the col- 19 Saul Kripke attempted to avoid these expanding hierarchies by postulating a procedure for semantic closure. In Kripke s view, the expanding hierarchies (using Tarski s truth predicate) would have to reach a fixed point, at which the expansion stopped. The continuing expansion would reach a point of diminishing returns, until further reinterpretations failed to add additional semantic value (Read ).